The present invention combines aspects of helicopter and fixed-wing propeller-driven aircraft design and aerodynamics. As will be seen, advances in control as developed particularly for quadcopters enable greater flexibility in flight modes and simplifications of mechanical and aerodynamic designs. Given the very large patent literature relevant to this invention, most of it being old and now basic to the education of VTOL engineers, this Background section will largely ignore the specifics of the patent literature and instead will recall known, applicable general concepts and terminology.
A motivating principle behind the present invention involves induced drag and its relationship to forward speed through the air. In low-subsonic aerodynamics, the significance of the formula for the induced drag of an ideal elliptic lift distribution is readily understood in terms of a picture. Viewing an airplane from directly behind, consider a circle whose diameter extends from wingtip to wingtip. As the aircraft moves forward, this circle sweeps out a cylinder of increasing volume and a corresponding rate of increase of contained air mass: d(air_mass)/d(time). As the pair of wings pushes down on the air it is passing through, a flat wing with an elliptic lift distribution across its span will encounter a downward velocity component, “induced_velocity.” Two applicable formulas are given:Lift=−d(momentum)/d(time) for downward momentum imparted to the airLift=−d(air_mass)/d(time)·induced_velocity for velocity of sinking air in the wing wake
For a wing with an elliptic spanwise lift distribution, the effective mass to which downward momentum is imparted is equivalent to the mass of air passing through this imaginary circle whose diameter matches the wingspan. As the aircraft moves faster, that circle sweeps through an increasing d(air_mass)/d(time), so for constant lift, the induced velocity decreases inversely with the increase in speed and swept air mass. Since the air mass is sinking down under the wings, the aircraft must effectively climb uphill through the sinking air in order to maintain level flight. Viewing the drag problem in terms of power, the power loss varies as the time derivative of mass multiplied by the square of the induced velocity:Power=d(energy)/d(time)=½·d(air_mass)/d(time)·(induced_velocity)2 
These formulas may vary by factors-of-2, depending on whether the induced velocity is specified at the wing or in the far wake, but the core principle is clear. To maintain constant lift, one must maintain a constant product of d(air_mass)/d(time) times (induced_velocity) while seeking to minimize the square-law power term. Induced drag is reduced as the craft travels faster through the air, so that more air mass is pushed down with a lesser induced velocity. This improvement in energy performance ceases at high speeds where the increase in form drag, varying roughly as the square of velocity, overtakes the decrease in induced drag. In a helicopter slowing to hovering flight, the fixed-wing induced drag formula ceases to be applicable. The rotary wings (e.g. two rotary wings for a two-bladed helicopter) cease to engage air mass with forward motion through the air. The spanwise horizontal-axis circle described above becomes a vertical-axis circle which is the swept diameter of the rotor. A relatively small d(air_mass)/d(time) is propelled directly downward with a correspondingly high velocity. Recalling the previous two equations, one sees that to maintain a constant lift according to the first equation while engaging a relatively low mass flow through the rotor at a correspondingly high velocity, the ratio of Power/Lift becomes large. A skilled helicopter pilot will minimize hovering and favor forward flight, where the helicopter's induced drag approaches the applicable fixed-wing formula. For a helicopter, the Aspect Ratio, defined as span2/area, becomes Diameter2/((π/4)·Diameter2)=4/π. This is obviously a low aspect ratio when compared to fixed-wing aspect ratios typically varying from 6 to 50. The rotor blade form drag associated with rotary forward flight is also particularly high, since the effective average tangential velocity of the rotor blade through the air must be significantly higher than the forward speed of the helicopter. In a single-rotor helicopter, the rotor blades traveling “backwards” opposite the direction of forward flight must have sufficient motion through the air to develop lift that balances that of the forward-moving rotor blade or blades. For a given rotational tangential tipspeed of the helicopter blades, a practical maximum forward flight speed is approximately 25% of that tipspeed. The maximum airspeed of the advancing rotor tip would therefore be roughly 4+1=5 times the forward speed, while for the receding (with the wind) rotor tip the airspeed multiple would be 4−1=3 times. The power dissipation associated with form drag of an airfoil varies roughly as the square of speed through the air, in the present example implying a power-dissipation multiple of 52=25 for the advancing wingtip and 32=9 for the receding wingtip. The energy dissipation multiples become more extreme at smaller radii, while the lack of adequate net airspeed to balance lift on the receding rotary wing becomes more extreme, thus setting the approximate 25% upper practical limit for forward speed as a fraction of tipspeed.
A comparison of rotary- versus fixed-wing aircraft energetics goes as follows. Consider aircraft of equal weight and where the rotor diameter matches the wingspan. In forward flight with equal engine power, the fixed-wing craft will fly more than twice as fast and achieve more than double the mileage. Clearly there is ample incentive to develop an aircraft combining the advantages of rotary-wing vertical takeoff and landing with efficient fixed-wing horizontal flight. Historic examples of such aircraft are seen in the experimental Bell Helicopter XV-3 and XV-15 aircraft, steps in the design lineage leading to the Bell-Boeing V-22 Osprey and the AgustaWestland AW609. In these related aircraft, vertical takeoff and low-speed horizontal flight are achieved with twin side-by-side helicopter rotors. An aircraft transitions to horizontal fixed-wing flight as the rotor planes tilt to provide increasing forward thrust, completing the transition with the rotors serving as propellers and fixed wings providing lift. Comparing similar aircraft, various models of the Bell UH-1 “Huey” series cruise between 120 and 140 knots, with the related, very high powered AH-1 “SuperCobra” having a cruise speed of about 150 knots and a maximum forward speed of 190 knots. A V-22 Osprey in airplane flight mode cruises at around 300 knots. The Osprey has separate systems for developing lift in its helicopter and airplane modes: two rotors for helicopter mode and wings for airplane flight. In helicopter mode, the wings interfere with the rotor downwash, with a substantial fraction of the wing chord hinging down and out of the way of the downwash as an oversize flap. In airplane flight, the rotors are extremely over-sized as propellers, while their twist is a compromise between relatively low twist for helicopter mode and much higher optimum twist for the high prop advance ratios of forward flight. The complexity, cost and high empty weight (in relation to wingspan and payload) of the Osprey are indications of the disadvantages of this aircraft design approach.
Other aircraft examples represent different compromises for achieving VTOL capability and forward flight in airplane mode. Harrier Jump Jets lift off by focusing downward thrust through a very small cross-section of airflow at very high downward velocity and very high power. To conserve fuel, this aircraft is forced to make quick transitions from takeoff to horizontal flight and back from horizontal flight to quick vertical landing.
There is a great need for an aircraft design that combines VTOL capability with the advantages of fixed-wing airplane-mode forward flight. The following Specification will teach such a physical design with its essential and optional degrees of freedom, along with a method for controlling its flight in VTOL and airplane modes and in transitions between the two modes.